The capacity of a wireless network could be considerably improved by employing directional antennas which are capable of illuminating multiple beams toward different directions. However, more beams from the same BS may lead to stronger inter-cell interference. In this paper, the authors consider coordinated beam scheduling schemes to mitigate the inter-cell interference. They first formulate this problem as a combinatorial optimization problem. They then reveal that the complexity of this problem hinges upon a single scalar termed as degree of constraint (DoC), which is related to the degree of conflict a beam is subject to. If the DoC is at least 3, the general beam scheduling problem is NP-hard.